Question

3) Radius of the circle is 13cm distance between chord and center of circle is 5cm find the length of the chord a) 12 cm b) 24 cm c) 16 cm d) 18cm​

Answer 1

Answer :

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This side also is the the distance of the chord from the center of the circle root (13^2 - 12^2) = root (5^2) = 5 cm. Let x-the distance of the chord from the center. length of chord=24 cms.

The radius of a circle is 13 cm

Given

radius = 13 cm

length of one of its chord = 10 cm

1/2 chord=10×1/2=5cm

Distance of the chord =

r

2

−l

2

=

13

2

−5

2

=

169−25

=

144

=

(12)

2

= 12. cm

∴ The distance of the chord = 12 cm.

Answer 2

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■ GIVEN THAT:-

RADIUS OF THE CIRCLE=13 cm

DISTANCE BETWEEN CHORD AND CENTRE OF THE CIRCLE=5cm

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■ TO FIND:-

LENGTH OF THE CHORD

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■ ACCORDING TO

QUESTION;-

Let AB be a chord of a circle with centre O and radius 13 cm.

Draw OL ⊥ AB.

Join OA.

Clearly,  OL = 5 cm and OA = 13 cm.In the right triangle OLA, we have

$OA ^{2}  = OL^{2}  + AL ^{2}$

$⇒   132 = 52 + AL^{2}$

$⇒ AL^{2}  = 144 cm^{2}$

$⇒ AL = 12 cm$

Since, the perpendicular from the centre to the chord bisects the chord. Therefore,AB = 2AL = (2 × 12) cm= 24 cm.

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HOPE IT HELPS YOU

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